After you insert new user with wp_insert_user(), you can call this wp_new_user_notification() function to send mail for newly registered users.
However, In order to customise them, you need to define this function and save it as a plugin of its own. But, it still have a chance that some other plugin (that is called before this) have control over it. So, the best way of customising it is saving it as a mu-plugin. Just create a folder ‘mu-plugins’ under wp-content and save it under a php filename.
Read more about mu-plugin here: https://codex.wordpress.org/Must_Use_Plugins